This article analyzes the dynamic process of price discovery in a competitive securities market where investors are equally informed about the fundamental determinants of an asset's end-of-period value but, because they do not know each other's wealth positions, do not know the equilibrium price of shares at the start of a current trading session. Because a large number of participants is assumed, issues concerning market impact and market manipulation are avoided. As trading progresses, participants update their expectations of an asset's equilibrium value. As they do so, price can either converge to a new level or, following a run, revert back to a previous level. This implies that, in clusters of adjacent prices, price changes are more apt to be predominantly of like sign (positive or negative) than would be the case under random walk with a bid-ask spread. Moreover, reversals, when they do occur, should be larger than continuations. An examination of 1988 transactions data for the 30 Dow Jones Industrial stocks shows that this is indeed the case. With the effect of the bid-ask spread removed, first-order autocorrelation coefficients are found to be positive.